What is the integral from 0 to 1 of 1/(t^2+1) ?

The integral from 0 to 1 of 1/(t^2+1) is pi/4

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integral from 0 to 1 of 1/(t^2+1)

\int_{0}^{1} \frac{1}{t ^{2} + 1} d t

\frac{π}{4}

Decimal

0.78539 \dots

Solution steps

\int_{0}^{1} \frac{1}{t ^{2} + 1} d t

Use the common integral:

\int \frac{1}{t ^{2} + 1} d t = arctan (t)

= [arctan (t)]_{0}^{1}

Compute the boundaries:

\frac{π}{4}

= \frac{π}{4}

What is the integral from 0 to 1 of 1/(t^2+1) ?
The integral from 0 to 1 of 1/(t^2+1) is pi/4